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arXiv:2208.07977

Towards the simulation of transition-metal oxides of the cathode battery materials using VQE methods

Marwa H. Farag, Joydip Ghosh

Published Aug 16, 2022• 0 citations
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Abstract

Variational quantum eigensolver (VQE) is a hybrid quantum-classical technique that leverages noisy intermediate scale quantum (NISQ) hardware to obtain the minimum eigenvalue of a model Hamiltonian. VQE has so far been used to simulate condensed matter systems as well as quantum chemistry of small molecules. In this work, we employ VQE methods to obtain the ground-state energy of LiCoO$_2$, a candidate transition metal oxide used for battery cathodes. We simulate Li$_2$Co$_2$O$_4$ and Co$_2$O$_4$ gas-phase models, which represent the lithiated and delithiated states during the discharge and the charge of the Li-ion battery, respectively. Computations are performed using a statevector simulator with a single reference state for three different trial wavefunctions: unitary coupled-cluster singles and doubles (UCCSD), unitary coupled-cluster generalized singles and doubles (UCCGSD) and k-unitary pair coupled-cluster generalized singles and doubles (k-UpCCGSD). The resources in terms of circuit depth, two-qubit entangling gates and wavefunction parameters are analyzed. We find that the k-UpCCGSD with k=5 produces results similar to UCCSD but at a lower cost. Finally, the performance of VQE methods is benchmarked against the classical wavefunction-based methods, such as coupled-cluster singles and doubles (CCSD) and complete active space configuration interaction (CASCI). Our results show that VQE methods quantitatively agree with the results obtained from CCSD. However, the comparison against the CASCI results clearly suggests that advanced trial wavefunctions are likely necessary to capture the multi-reference characteristics as well as the correlations emerging from high-level electronic excitations.

DOI
10.48550/arxiv.2208.07977

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Variational quantum eigensolver (VQE) is a hybrid quantum-classical technique that leverages noisy intermediate scale quantum (NISQ) hardware to obtain the minimum eigenvalue of a model Hamiltonian. VQE has so far been used to simulate condensed matter systems as well as quantum chemistry of small molecules. In this work, we employ VQE methods to obtain the ground-state energy of LiCoO2_22​, a candidate transition metal oxide used for battery cathodes. We simulate Li2_22​Co2_22​O4_44​ and Co2_22​O4_44​ gas-phase models, which represent the lithiated and delithiated states during the discharge and the charge of the Li-ion battery, respectively. Computations are performed using a statevector simulator with a single reference state for three different trial wavefunctions: unitary coupled-cluster singles and doubles (UCCSD), unitary coupled-cluster generalized singles and doubles (UCCGSD) and k-unitary pair coupled-cluster generalized singles and doubles (k-UpCCGSD). The resources in terms of circuit depth, two-qubit entangling gates and wavefunction parameters are analyzed. We find that the k-UpCCGSD with k=5 produces results similar to UCCSD but at a lower cost. Finally, the performance of VQE methods is benchmarked against the classical wavefunction-based methods, such as coupled-cluster singles and doubles (CCSD) and complete active space configuration interaction (CASCI). Our results show that VQE methods quantitatively agree with the results obtained from CCSD. However, the comparison against the CASCI results clearly suggests that advanced trial wavefunctions are likely necessary to capture the multi-reference characteristics as well as the correlations emerging from high-level electronic excitations.
We present numerical calculations of the energetic separation between different spin states (singlet, triplet and quintet) for a simplified model of a deoxy-myoglobin protein using the variational quantum eigensolver (VQE) algorithm. The goal is to gain insight into the workflow and challenges of VQE simulations for transition metal complexes, with emphasis on methodology over hardware-specific implementation. The numerical calculations are performed using an in-house statevector simulator with single- and multi-reference trial wavefunctions based on the k-unitary pair coupled-cluster generalized singles and doubles or k-UpCCGSD ansatz. The spin-state energetics for active spaces of increasing size up to 10 spatial orbitals (20 spin orbitals or qubits) are computed with VQE and were found to agree with the classical complete active self-consistent field or CASSCF method to within 1-4 kcal/mol. We evaluate relevant multi-reference diagnostics and show that the spin states computed with VQE possess a sufficient degree of multi-reference character to highlight the presence of strong electron correlation effects. Our numerical simulations show that in the ideal case, the VQE algorithm is capable of reproducing spin-state energetics of strongly correlated systems such as transition metal complexes for both single- and multi-reference trial wavefunctions, asymptotically achieving good agreement with results from classical methods as the number of active orbitals increases.
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High Resolution Image Download MS PowerPoint Slide Quantum computers have the potential to efficiently solve the electronic structure problem but are currently limited by noise and shallow circuits. We present an enhanced Variational Quantum Eigensolver (VQE) ansatz based on the Qubit Coupled Cluster (QCC) approach that requires optimization of only n parameters, where n is the number of Pauli string generators, rather than the typical n + 2 m parameters, where m is the number of qubits. We evaluate the ground state energies and molecular dissociation curves of strongly correlated molecules, namely O 3 and Li 4, using active spaces of varying sizes in conjunction with our enhanced QCC ansatz, Unitary Coupled Cluster Single–Double (UCCSD) ansatz, and the classical Coupled Cluster Singles and Doubles (CCSD) method. Compared to UCCSD, our approach significantly reduces the number of parameters while maintaining high accuracy. Numerical simulations demonstrate the effectiveness of our approach, and experiments on superconducting and trapped-ion quantum computers showcase its practicality on real hardware. By eliminating the need for symmetry-restoring gates and reducing the number of parameters, our enhanced QCC ansatz enables accurate quantum chemistry calculations on near-term quantum devices for strongly correlated systems.
Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.